Underlying monoid of a commutative monoid

Exercise 5.3.12. Let \(M\colon \Span (\Fin ) \to C\) be a commutative monoid. Show that \(M \circ \Cut \colon \simp \catop \to C\) defines a monoid in \(C\), whose multiplication agrees with the addition map of \(M\). Deduce that \(M \circ \Cut \) is a group if and only if \(M\) is a commutative group, and that there is a pullback square

In particular, we obtain forgetful functors \[ U := \Cut ^*\colon \CMon (C) \to \Mon (C) \qquadtext { and } U := \Cut ^*\colon \CGrp (C) \to \Grp (C). \]